IOs is a bit of an issue, with the licencing requirements currently insisting on building on a (recent) Mac. I'm just starting out with Xamarin so at some point I'll need to bite the bullet and get access to one too.
As Jake mentioned, there are some publicly accessible Macs which might be your best bet for getting started although I hate to imagine how locked down they will be. How cheeky are you, and how big is your app? Maybe you could ask for test drive in an Apple store and build your app there?